One Earth, Two Carbon-Emission Tax Rates

The increasing environmental impact of supply-chain activities has intensified interest in carbon-regulation policies such as carbon taxes. This paper analyzes a two-echelon manufacturer–retailer system operating under decentralized decision making, where both parties independently optimize their decisions while facing potentially different carbon tax rates. We develop a production-inventory model that incorporates emissions-related costs, with the retailer determining the ordering cycle-length and the manufacturer selecting number of deliveries per production cycle. We derive analytical results that characterize the optimal decentralized decisions and identify conditions under which the structure of the solution changes. The analysis provides clear threshold conditions under which the optimal replenishment strategy simplifies to a lot-for-lot ordering pattern. We further find that raising the retailer’s carbon tax rate beyond a critical level does not induce additional emission reductions for either supply-chain member; rather, it only imposes a greater financial burden on the retailer. Extending the analysis to the manufacturer, we show that shipping decisions are governed by the interaction between emission-related and operational cost parameters. The results indicate that carbon taxes affect environmental performance only indirectly by triggering changes in discrete operational changes. Again, raising the manufacturer’s carbon tax rate may fail to generate additional emission reductions beyond certain threshold levels. A comprehensive numerical study illustrates the sensitivity of costs and emissions to key parameters, including tax rates and emission coefficients. The results highlight the role of shipment frequency and production rate as important operational levers for achieving both economic and environmental improvements. Overall, the findings provide insights into the effectiveness of carbon taxation and offer managerial and policy implications for designing sustainable supply-chain systems under decentralized control.